dpprfs(3P) Sun Performance Library dpprfs(3P)NAMEdpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE DPPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR,
WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
SUBROUTINE DPPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
F95 INTERFACE
SUBROUTINE PPRFS(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
SUBROUTINE PPRFS_64(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void dpprfs(char uplo, int n, int nrhs, double *a, double *af, double
*b, int ldb, double *x, int ldx, double *ferr, double *berr,
int *info);
void dpprfs_64(char uplo, long n, long nrhs, double *a, double *af,
double *b, long ldb, double *x, long ldx, double *ferr, dou‐
ble *berr, long *info);
PURPOSEdpprfs improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solu‐
tion.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) =
A(i,j) for j<=i<=n.
AF (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by DPPTRF/ZPPTRF,
packed columnwise in a linear array in the same format as A
(see A).
B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPPTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X). If XTRUE is
the true solution corresponding to X(j), FERR(j) is an esti‐
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele‐
ment in X(j). The estimate is as reliable as the estimate
for RCOND, and is almost always a slight overestimate of the
true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any ele‐
ment of A or B that makes X(j) an exact solution).
WORK (workspace)
DOUBLE PRECISION array, dimension(3*N)
WORK2 (workspace)
INTEGER array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 dpprfs(3P)
